Is it permissible for a woman to correct the Imam during the prayer?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

The permissibility of correcting the Imam indicates that the ruling includes both men and women.

Ash-Shawkani said:

"Evidence proves that correcting the Imam is unrestrictedly permissible. Thus, if the Imam forgets a verse in an audible recitation, then correcting him is to remind him of the verse that he has forgotten, as indicated by the Hadeeth used as proof of this issue. If the Imam forgets a pillar of the prayer, then he should be corrected by saying tasbeeh on the part of men or by clapping the hands on the part of women."

Correcting the Imam may be obligatory in some cases where the validity of the prayer is conditional on doing so, as in the case when the Imam does not recite Al-Fatihah properly in full. Ar-Ruhaybani, a Hanbali scholar said:

It is obligatory for the person to correct the Imam if he is confused or makes a mistake such as forgetting to prostrate, in which case he is required to notify him because the validity of his prayer is contingent on performing such an action. Also, if the Imam is unable to complete the recitation of Al-Fatihah, then his prayer is rendered invalid.

Al-Mawwaq, a Maaliki scholar said, "Maalik said in Al-Mudawwanah that if the Imam stops (because of forgetting a verse) while reciting in the prayer, he should be reminded by those who pray behind him."

Based on this, there is nothing wrong with a woman correcting the Imam. However, if the Imam is a non-mahram (permanently unmarriageable) to her, or if there are other men present who are non-mahram to her, then she should not undertake to do this unless no man is available to do it. 

Allah knows best.